(d^2)/(dx^2)(cos(x)+sin(x)+1/2 x^2+1/x)

Lösung

\frac{d ^{2}}{d x ^{2}} (cos (x) + sin (x) + \frac{1}{2} x^{2} + \frac{1}{x})

- cos (x) - sin (x) + 1 + \frac{2}{x ^{3}}

Schritte zur Lösung

\frac{d ^{2}}{d x ^{2}} (cos (x) + sin (x) + \frac{1}{2} x^{2} + \frac{1}{x})

Vereinfache

cos (x) + sin (x) + \frac{1}{2} x^{2} + \frac{1}{x} : cos (x) + sin (x) + \frac{x ^{2}}{2} + \frac{1}{x}

= \frac{d ^{2}}{d x ^{2}} (cos (x) + sin (x) + \frac{x ^{2}}{2} + \frac{1}{x})

\frac{d}{d x} (cos (x) + sin (x) + \frac{x ^{2}}{2} + \frac{1}{x}) = - sin (x) + cos (x) + x - \frac{1}{x ^{2}}

= \frac{d}{d x} (- sin (x) + cos (x) + x - \frac{1}{x ^{2}})

\frac{d}{d x} (- sin (x) + cos (x) + x - \frac{1}{x ^{2}}) = - cos (x) - sin (x) + 1 + \frac{2}{x ^{3}}

= - cos (x) - sin (x) + 1 + \frac{2}{x ^{3}}

\frac{d}{d x} (2 (sin (x))^{2})

\int \frac{x ^{3 k}}{k !} d x

x \to \frac{1}{5} lim (2 + ∣ 5 x - 1 ∣)

\int 2 e^{y} d y

d er i v a t i v e (5 x^{2} - x + 11)^{\frac{3}{2}}